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A Classic. But that does not make it excellent
on May 1, 2003
I am pretty much interested in geometry. I am, in fact, enthusiastic, and enthusiastic people usually do have strange habits regarding their subjects of enthusiasm. I, for one, like to buy all of the geometry books I can lay my hand on regardless of its relevance to my studies or usefulness for reading.
And this book, being a classic, was on top of my demanded books list until I bought it around 1998. As usual with these books, I postponed its reading until the new millennium. But when I read it I was very disappointed.
The material of this book is one of the most beautiful afforded by a mathematics book. It is very interesting, but, alas, it is written in a forbidding notation. I can understand high level math books in Algebra and Analysis, but this book confused me with words. Frankly, I do not see why a math book is supposed to explained in words after all this development of mathematics.
Unfortunately, most historian mathematicians disagree with my view. They see that writing the elements of Euclid (The first rigorous set of axioms and lemmas) in the modern notation is unfaithful to the original manuscript. Well, I have got no problem with that, but at least try to make it up to date so that people could go through it.
You see that I gave it 4 stars. Yes the material of the book was excellent, and it rather deserved 5 stars, but for this tedious presentation.
One other thing I hated a bout this volume was the introduction. It had taken about one third of the book, and after the definitions of the first book, there are notes on the definitions and postulates that take another third of the book. These notes are not all that easy and at a higher level than the postulates of Euclid, and I found them irrelevant. I do not understand here why did not the author, who made notes on the definitions, make a section explaining all the postulates in modern notation.
As for the material, the volume covers Books I and II of Euclid's 13 books of the elements. The first book introduces a set of definitions and goes on characterizing triangles. It, even, proves the Pythagorean theorem. This proof was a bit difficult, a simpler proof can be found else where, but, after all, it is amazing how mathematicians could have solved such a problem thousands of years ago.
He introduced the famous constructions of straight edge and a compass, he would construct an isosceles triangle starting from a given segment by merely using a straight edge and a compass. Later on, Galois studied this construction in his famous Galois theory (try Artin's Galois theory, although I do not guarantee it).
The second books deals with areas of triangles and rectangles, and Euclid's notation shows it incompetence when he uses the same name for two different things. For in the first book he used to say that two triangles are equal if all their angles and sides are equal, but in the second book he would define two triangles to be equal if they had the same area!
All in all, I enjoyed the book, and would have enjoyed it more if not for the drawbacks.